But long term, we're committing to meters of sea level rise.

Although the general outlines of climate change are a matter of basic physics, many of the details rely on a complex interplay of factors—some of which are still not thoroughly understood. For example, it's clear that a warmer world will mean larger sea levels. The oceans expand with heat, and land-based glaciers and ice sheets melt, dumping their water into the seas. But the exact rate of sea level rise and its ultimate end-point remain active areas of research.

This week, two papers have been released that bring some clarity to the situation. One of them looks at where the ocean levels are likely to end up centuries from now, when our planet is equilibrated to its altered climate. And the second looks at a warning sign of rising seas—the loss of ice from Greenland and Antarctica—but concludes there's no way to tell if that process is accelerating yet.

Trend spotting

We'll hit the ambiguous result first. Up until recently, it was very difficult to make an accurate estimate of the volume of ice present in the world's biggest ice sheets on Antarctica and Greenland. That changed with the launch of the GRACE mission, which can track the gravitational pull of the ice on orbiting satellites, providing a measure of the mass they contain. Since GRACE started taking data on the ice sheets in 2003, both ice sheets have clearly been shrinking. There have been some indications that the loss was accelerating, though different studies produced different values for the speed-up.

In the new study, researchers stepped back and looked at the bigger picture: how varied is the behavior of the ice sheets and, given that variability, how long would we need to look before we could detect a trend? As the authors note, things like a warming climate impose a long-term melting trend on the ice sheets. But superimposed on that is what they term ice sheet "weather"—shorter term influences that add noise to the trend, like the actual weather and changes in ocean circulation. Over short time periods, these events can completely obscure any long-term trends.

Just how short? The authors used non-GRACE data to model the ice sheets' behavior over long periods. They also statistically analyzed the data from GRACE, looking at how longer and shorter observations changed the size of any apparent trends. All of the work agreed that the decade of GRACE data is enough to determine that the ice sheets are clearly shrinking. But the ice sheet weather is enough to keep us from detecting any significant acceleration. For the Antarctic, the ice's behavior is steady enough that we're on the verge of being able to detect an acceleration of 10 Gigatonnes (Gt) a year. But for Greenland, we'd need another decade of observations for that to stand out above the noise.

Most current estimates of the acceleration are above 10Gt a year though, so we may not have to monitor for quite that long. Still, it provides a strong argument for continuing GRACE's mission.

Thinking long-term

For the most part, the focus on sea level rise has been framed in terms of the reports of the Intergovernmental Panel on Climate Change, which attempts to predict what we'll see by the end of the century. But the sorts of processes that influence the rising seas—transferring heat into the oceans and melting ice—have a tremendous inertia. Even if temperatures were to stabilize by the end of the century, the seas would go on rising, probably for centuries, before stabilizing again.

The obvious question is where they would stabilize. Here, history provides a disturbing answer. At several points in the past, when temperatures were just a few degrees Celsius above the pre-industrial climate, the ocean levels were several meters above what they are currently—in some cases well over 10 meters.

To understand how this could come about, the authors modeled the major factors influencing sea level rise independently. For the thermal expansion of the oceans, the authors ran six coupled climate models forward for 10,000 years, determining that thermal expansion would add 0.4m of sea level for each degree Celsius. Mountain glaciers also contribute, but there's simply not that much water trapped in those that are at low enough altitudes to completely melt. Their total possible contributions are capped at 0.6 m. A model of the Antarctic ice balance suggests it will provide a relatively steady contribution of 1.2m for each degree Celsius.

The wild card in all of this is Greenland. After a relatively smooth rise over a single degree Celsius, Greenland dumps over four meters of ocean level over the span of about half a degree. Although this represents a major loss of ice, there's enough left for a steady contribution as temperatures continue to warm.

Combined, these factors add up to about 2.3m of sea level rise for each degree above preindustrial levels, a rate that should hold for over four degrees of a warming climate. Included in that average, however, is the rather sudden rise triggered by the melting of Greenland. To see whether the values produced by their models were reasonable, the authors compared the output with historic sea level readings from periods where the Earth was somewhat warmer than at present: the middle Pliocene and two earlier interglacial periods. These estimates are rather uncertain (for example, middle Pliocene sea levels have been measured at anywhere between five and 30 meters above the present ones), but all of them encompass the values produced by the authors' model.

Assuming the authors' value of 2.3m/°C is roughly on-target, it's clear that we haven't seen much of the sea level rise that our existing carbon emissions will ultimately trigger. We probably won't see them by the end of the century, either. That's the good news. The bad news is that, at our current trajectory, we're likely to put the climate in a state where well over 10m of sea level rise will be inevitable.